1. Field of the Invention
The present invention relates to a coreless rotary electric appliance, and more particularly to a coil winding method for forming a cup-shaped coil body open at an end face thereof with a continuous wire comprising inclined coil wire portions wound along the cylindrical periphery of said coil body and connected in succession by end connecting wire portions arranged on an end face of said coil body, and to a rotary electric appliance utilizing such coil winding method.
2. Description of the Prior Arts
There are already proposed various methods for forming a cup-shaped rotary coil, and the present applicant disclosed, in the Japanese Patent Publication Sho No. 49-22361, a winding method for a double-layered cup-shaped coil in which inclined coil wire portions arranged with a determined inclination angle along the cylindrical periphery of the coil body are connected in succession by end connecting wire portions arranged only on one end face of said coil body.
In a so-called magnet DC motor utilizing a permanent magnet as the field magnet, the suitable selection of the DC resistance R, effective conductor number Z and effective magnetic flux .phi. of the armature is indispensable for designing a motor of a desired performance. Among the iron loss, copper loss and mechanical loss which constitute three major losses in the DC motor, the iron loss can be rendered practically negligible by the use of a coreless rotor, since the hysteresis loss resulting from alternation of the magnetic flux does not exist in this case and the eddy current loss on the stator side is also negligibly small. Also such coreless structure significantly reduced the reactance voltage induced in the coil by the commutation due to the absence of iron core, thus realizing almost ideal commutation and achieving a stabler function and a longer service life of the commutating mechanism.
Such motor well satisfies the following theoretical equation for a motor circuit without iron loss: EQU IaV-Ia.sup.2 R=IaEc (1)
wherein
V:input terminal voltage PA0 Ia:armature current PA0 Ec:inverse electromotive voltage PA0 R:Ra+Rb PA0 Ra:armature resistance PA0 Rb:brush contact resistance.
Thus, the output IaEc can be increased by minimizing the copper loss Ia.sup.2 R with respect to a given value of input IaV by suitable designing, and it is rendered easily possible to obtain a highly efficient motor if the mechanical loss included in said output IaEc is satisfactorily controlled. In certain applications, however, the method of appropriately determining the above-mentioned parameters R, Z and .phi. becomes important in order to achieve desirable revolution and other characteristics of the motor. In the known methods of forming a cylindrical cup-shaped coil without end connecting wire portions on both end faces thereof as shown in FIG. 2, such as disclosed in the U.S. Pat. No. 3,360,668, DAS No. 1,188,709 or Japanese Patent Publication Sho No. 38-2151, the winding width So' which determines the effective number of conductors as shown in FIG. 3 becomes severely limited if it is desired to obtain a flatter coil with a smaller inclination angle .theta. of the effective coil portions as shown in FIG. 1.
In FIG. 3 the winding width So per segment is given by the peripheral length of the rotor divided by the number of commutator segments, and the number of conductors in said winding width So corresponds to the number of coil turns in a core slot in case of an iron core rotor. Furthermore, for a given value of So, the effective winding width So' is given by the equation So'=So.multidot. sin .theta. and thus depends upon the inclination angle .theta. of the coil. Naturally the angle .theta. should be constant over the entire coil, and, if not, the effective winding width So' is limited by the minimum value of .theta.. The coil therefore assumes a helical trajectory with a constant inclination along the cylindrical surface of the armature. In order to wind a given effective number of conductors within said effective winding width So' it becomes necessary to employ a wire of smaller diameter for a flatter coil even if the diameter dm of the armature remains constant, thus resulting in an increased copper loss and thus a lowered efficiency, due to the increased armature resistance Ra in the foregoing motor equation.
The coil structure disclosed by the present applicant in the Japanese Patent Publication Sho No. 49-22361 is provided with end connecting wire portions on one end face of the coil body as shown in FIG. 4, whereby the inclination angle .theta. of the coil wire portions on the cylindrical periphery can be arbitrarily determined and need not be decreased in proportion to the flattening of the coil body. In this manner it is rendered possible, by suitably determining the angle .theta. as a function of the armature resistance Ra, effective conductor number Z and effective total flux .phi., to prevent severe limitation on the effective winding width So' in a conventional flat coil and thus to avoid the increase in the armature resistance Ra.
As an example, the coil resistance Ra for a coil with an average diameter dm of 29.4 mm, a coil height lc of 18 mm, five commutator segments and 240 effective conductors is 2.23.OMEGA. for the coil structure shown in FIG. 1 and 0.66.OMEGA. for the coil structure shown in FIG. 4.
In the above-mentioned calculation it is supposed that the fold-back points A and C of the wire portions are in the diametrically opposed positions, and that the connecting portion AC is wound along the upper brim of the cup-shaped coil body. However it is also possible to connect the points A and C with a linear or quasi-linear end connecting portion constituting a chord on the upper end face of said coil body, in order to further reduce the resistance Ra without affecting the effective value of Z.multidot..theta. as shown in FIG. 5. In such structure the distance ABCA which is equal to 10.4 cm in the structure of FIG. 4 is reduced to 0.2 cm, whereby the resistance Ra is reduced from 0.66.OMEGA. to 0.59.OMEGA. corresponding approximately a quarter of the resistance in the conventional structure.
In this manner the invention disclosed in the Japanese Patent Publication Sho No. 49-22361 was principally aimed at the improvement in R and Z among three major motor parameters, but the present inventors found that the coil area intersecting the magnetic flux can be controlled by suitably selecting the end connecting positions, as detailedly disclosed in DOS No. 2,126,199. According to this invention the above-mentioned fold-back points A and C need not be in diametrically opposite positions but can be suitably positioned according to the extent of flattening of the coil.
In the foregoing example on which the resistance has been calculated, the end connecting points are in diametrically opposite positions. However a maximum coil area can be obtained by displacing the position .chi. in FIG. 8 to the negative side on the axis X-X' while the coil winding rate can be increased despite of the reduced coil area if the position X is displaced to the positive side. In the following there is described the determination of the maximum coil area. It is known that, when a closed circuit formed of an arbitrary closed curve is placed in a uniform parallel magnetic field, the moment developed in said circuit along any arbitrary axis is proportional to the area of the projection of said closed circuit onto a plane parallel to said axis and to the direction of magnetic field. FIG. 6 shows the relationship between the projected coil area and the end connecting positions in case of the coils as shown in FIGS. 5 and 8, wherein the center angle .alpha. or 2.pi.-.alpha. corresponding to the end connecting points A, C is defined as the end connection angle.
In the following calculation, the tangent of the inclination angle of the helical curve L is defined as k. .gamma. shown in FIG. 6 represents the position of coil in cylindrical coordinate. EQU Z=r.gamma.k (1) EQU y=r.multidot.sin .gamma.=R.multidot.sin z/rk (2)
The equation (2) indicates that the projection of the curve L is a sinusoidal curve. By numerical calculation the torque T(t) generated in a one-turn elementary coil can be represented by the following equation: EQU T(t).sub.max =1.45 rlBI (3)
wherein .alpha.=92.92.degree..about.92.94.degree..apprxeq.93.degree., B=magnetic flux density of gap, and I=current conducting through coil. In the coil shown in FIG. 7 which corresponds to a case of t=1 in FIG. 6: EQU T(1)=1.27 rlBI (4)
Also in case of t=1/2 corresponding to the end connections at diametrically opposite positions: EQU T(1/2)=1.27 rlBI (5)
In this manner these two coils provide a same area, but the latter is advantageous in the winding rate because of the larger angle .theta..
In summary, in a cup-shaped armature coil open at an end thereof the end connecting portions on an end face provides the freedom of freely selecting the parameters R, Z and .phi. without affecting the structural performance as the cup-shaped rotor.